The nonequilibrium temperature in the kinetic theory of gases is reexamined and an alternative definition of the temperature in terms of the local equilibrium distribution function is proposed. The alternative definition introduces a new physical quantity, 'exoenergy,' which represents the nonequilibrium nature of thermodynamic systems. The internal energy equation is split into two equations, the temperature equation and the exoenergy equation. https://www.selleckchem.com/products/Obatoclax-Mesylate.html In order to rationalize the equation splitting, the nonequilibrium thermodynamics is considered introducing the nonequilibrium entropy phenomenologically. The proposed temperature equation resolves the overshooting anomaly of temperature profiles of the Monte Carlo data for one-dimensional normal shock waves. The exoenergy equation makes the theory self-consistent and gives the entropy production of shock waves in closed form. The theory gives a general form of the shock wave equation and the general relation of the bulk viscosity to the shear viscosity and the heat conductivity of dilute monatomic gases.A ground-state phase diagram for a three-layered Heisenberg ferromagnet with magnetic anisotropy and dipole-dipole interactions is inferred from a linear analysis of the fastest growing mode for the time-dependent Ginzburg-Landau equation. It is also investigated numerically by solving the Landau-Lifshitz equation for the model. The phase diagrams obtained from the two methods resemble each other. There is an in-plane ferromagnetic state, and states with out-of-plane stripe orders. Although the phase diagram is qualitatively similar to that for the corresponding two-dimensional model, the region of the in-plane ferromagnetic state shrinks considerably compared to that for the two-dimensional model.We derive a general lower bound on distributions of entropy production in interacting active matter systems. The bound is tight in the limit that interparticle correlations are small and short-ranged, which we explore in four canonical active matter models. In all models studied, the bound is weak where collective fluctuations result in long-ranged correlations, which subsequently links the locations of phase transitions to enhanced entropy production fluctuations. We develop a theory for the onset of enhanced fluctuations and relate it to specific phase transitions in active Brownian particles. We also derive optimal control forces that realize the dynamics necessary to tune dissipation and manipulate the system between phases. In so doing, we uncover a general relationship between entropy production and pattern formation in active matter, as well as ways of controlling it.We characterize equilibrium properties and relaxation dynamics of a two-dimensional lattice containing, at each site, two particles connected by a double-well potential (dumbbell). Dumbbells are oriented in the orthogonal direction with respect to the lattice plane and interact with each other through a Lennard-Jones potential truncated at the nearest neighbor distance. We show that the system's equilibrium properties are accurately described by a two-dimensional Ising model with an appropriate coupling constant. Moreover, we characterize the coarsening kinetics by calculating the cluster size as a function of time and compare the results with Monte Carlo simulations based on Glauber or reactive dynamics rate constants.Complex problems of social interaction are usually studied within the framework of agent-based models. Some of these problems, such as issue alignment and opinion polarization, are better suited in the framework of n-dimensional opinion space. Although this kind of complex problem may be explored by numerical simulations, these simulations can hinder our ability to obtain general results. In this work, we show how, under certain conditions, a classical multidimensional opinion model such as the Axelrod model can give rise to a closed set of master equations in terms of vector similarities between agents. The analytical results fully agree with the simulations on complete networks, accurately predict the similarity distribution of the whole system in sparse topologies, and provide a good approximation of the similarity of physical links that improves when the mean degree of the system increases.The hyperuniformity concept provides a unified means to classify all perfect crystals, perfect quasicrystals, and exotic amorphous states of matter according to their capacity to suppress large-scale density fluctuations. While the classification of hyperuniform point configurations has received considerable attention, much less is known about the classification of hyperuniform two-phase heterogeneous media, which include composites, porous media, foams, cellular solids, colloidal suspensions, and polymer blends. The purpose of this article is to begin such a program for certain two-dimensional models of hyperuniform two-phase media by ascertaining their local volume-fraction variances σ__V^2(R) and the associated hyperuniformity order metrics B[over ¯]_V. This is a highly challenging task because the geometries and topologies of the phases are generally much richer and more complex than point-configuration arrangements, and one must ascertain a broadly applicable length scale to make key quantities dcedures.We examine theoretically and numerically fast propagation of a tensile crack along unidimensional strips with periodically evolving toughness. In such dynamic fracture regimes, crack front waves form and transport front disturbances along the crack edge at speed less than the Rayleigh wave speed and depending on the crack speed. In this configuration, standing front waves dictate the spatiotemporal evolution of the local crack front speed, which takes a specific scaling form. Analytical examination of both the short-time and long-time limits of the problem reveals the parameter dependency with strip wavelength, toughness contrast and overall fracture speed. Implications and generalization to unidimensional strips of arbitrary shape are lastly discussed.Cell type-specific gene expression patterns are represented as memory states of a Hopfield neural network model. It is shown that order parameters of this model can be interpreted as concentrations of master transcription regulators that form concurrent positive feedback loops with a large number of downstream regulated genes. The order parameter free energy then defines an epigenetic landscape in which local minima correspond to stable cell states. The model is applied to gene expression data in the context of hematopoiesis.